The Language of Mathematics by Robert L. Baber

The Language of Mathematics: Utilizing Math in Practice

by Robert L. Baber

last modified 2012 February 8

All rights to the material on this web page
are reserved by the author, Robert L. Baber.

This book was published by John Wiley & Sons, Inc., September 2011.
You can order The Language of Mathematics: Utilizing Math in Practice from any bookseller.

Background and my reasons for writing this book

The first step in solving mathematically a problem stated in English is to reformulate the English text into a mathematical model. The second step is solving the mathematical model. The first step is usually presumed to be part of the mathematical problem, but actually, it is a translation problem – a language problem. This first step requires fluency in both English and the Language of Mathematics and the ability to translate between the two. This book will help the reader to acquire the necessary knowledge and skills.

My experience learning, using and teaching others mathematics and how to use it in practice has convinced me that looking at mathematics as a language can facilitate the learning process, understanding and the ability to apply mathematics in practice. I believe that it can even enable some people to learn how to use mathematics effectively who would otherwise be completely turned off mathematics by their early exposure to it – and there are many such people in today's world.

In order to reason logically about things, mathematicians have developed a particular language with particular characteristics. That language – the Language of Mathematics – and other languages developed by human societies are similar in some respects and different in some ways.

What is mathematics? Someone once answered that question with "What mathematicians do". That, of course, begs the question, "What do mathematicians do?" They reason logically about things – artificial, abstract things.

Many of those things, although artificial and abstract, are useful in modelling actual things in the real world, for example

structures of buildings, dams, bridges, roads, etc.
mechanical devices and equipment
machines, engines and all kinds of energy conversion devices and systems
vehicles of all types – land, underwater, water surface, air, space
electrical circuits, devices and equipment for many different applications
communication systems – wired and wireless – and their components
systems for cryptography
molecules, atoms, nuclei, subatomic particles
chemical reactions and chemical reactors
systems for generating and distributing electrical power
nuclear decay and interaction processes, nuclear reactors
heating and cooling systems
computer software
economies (production, consumption, imports, exports, trade, income, employment, prices, etc.)
financial and economic markets (prices, trading volumes, options, derivative instruments, risk assessment, etc.)
business systems and processes (sales, inventories, various assets and liabilities, etc.)
astronomical systems, processes and phenomena
atmospheric processes and phenomena
ecological systems and processes
geological processes and phenomena
biological systems and processes
structural aspects of languages, natural and artificial
etc., etc.

Such models enable us to understand, describe and predict things in the real world better, to our considerable benefit.

To help others to learn mathematics or to improve their ability to apply it beneficially in their own work, I have written a book on mathematics as a language. This book will be of interest to the following groups of readers:

engineers, consultants, managers, scientists, technicians and others who could benefit vocationally and professionally by a greater ability to use and apply mathematics in their work
students in tertiary educational institutions
students in secondary schools especially interested in mathematics, science or languages
designers of mathematics curricula and teaching materials for students at all levels
teachers of mathematics, science or languages in tertiary educational institutions (universities, polytechnics and vocational and technical schools)
teachers of mathematics, science or languages in secondary schools
teachers in primary schools who introduce pupils to mathematics and especially to word problems
persons with a general or an intellectual interest in mathematics, science or language